In this work powerful numerical methods were used to study several problems that still remain unsolved in TMS.The first problem that was studied is related to the difficulties that arise when stimulating sub-cortical deep regions with TMS, due to the fact that the induced field rapidly decays and loses focality with depth. This study's approach to overcome this difficulty was to combine ferromagnetic cores with a coil designed to induce an electric field that decays slowly. The efficacy of this approach was tested by using the FEM to calculate the field induced by this coil / core design in a realistically shaped head model. The results show that the core might make this coil even more suited for deep brain stimulation.The second problem that was tackled is related to the lack of knowledge about the dominant mechanisms through which the induced electric field excites neurons in TMS. In this work the electric field along lines, representing trajectories of actual cortical neurons, was calculated using the FEM. The neurons were embedded in a realistically shaped sulcus model, with a figure-8 coil placed above the model. The electric field was then incorporated into the cable equation. The solution of the latter allowed the determination of the site and threshold of activation of the neurons. The results highlight the importance of axonal terminations and bends and tissue heterogeneities on stimulation of neurons.The third problem that was studied concerns TMS of small animals and the lack of knowledge about the optimal geometry, size and orientation of the used coils. This was studied by using the FEM to calculate the electric field induced in a realistically shaped mouse model by several commercially available coils. The results showed that the smaller coils induced fields with higher magnitude, better focality, and smaller decay than the bigger coils.These results highlight the importance of numerical modelling in TMS, either in coil design, determination of basic neurophysiologic mechanisms or optimization of experimental procedures.